Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int main(){
	int n,a[1000];
	double ma = -1.0;
	cin >> n;
	for(int i = 0;i < n;i++) cin >> a[i];
	sort(a,a + n);
	for(int i = 0;i < 3;i++){
		for(int j = 0;j < n - i - 1;j++){
			int b = j,c = j + i + 1,d = -1,e,used[1000] = {};
			used[b] = true;
			used[c] = true;
			for(int k = n - 1;k >= 0;k--){
				if(!used[k]){
					if(d == -1) d = k;
					else{
						e = k;
						break;
					}
				}
			}
			ma = max(ma,(double)(a[d] + a[e]) / (double)(a[c] - a[b]));
		}
	}
	printf("%.9lf\n",ma);
	return 0;
}